Script
Mathematics, English for Sek I and Sek II
Mathematica - The Principles of Math
6. The Mysteries of Multiplication and Exponents
09:55 minutes
00:30 (caption)
How far is the Andromeda constellation from Earth?
00:35 (caption)
1017 = the number 10 multiplied by itself 17 times
“Exponentiation”
01:05 Let’s say you present roses to your sweetheart every day. On
the first day, you start by presenting a single flower. The next day, the
number of roses is doubled. How many flowers would you end up
presenting on the fifth day?
01:14 (caption)
first day - a rose
second day - two roses
third day - four roses
fourth - eight roses
fifth day - sixteen roses
01:31 The number of roses doubles each day. On the fifth day, you
would need to prepare sixteen roses.
01:38 But if you’re confused by multiplying by two so many times, you
can simply use exponents.
Put four to the upper right of two and it reads, “two to the power of
four,” or, “two to the fourth power.” That means you need to multiply
two by itself four times.
01:52 24 roses = 16 roses
02:00 Exponentiation refers to a math operation in which the same
number is multiplied by itself several times.
02:07 In an exponential operation, the number being multiplied is called the base and the times it is multiplied by itself is called the exponent.
02:10 (caption)
base exponent
02:21 It was the Dutch mathematician Simon Stevin who first adopted
the concept of exponents.
02:21 (caption)
Simon Stevin (1548/49 – 1620)
Dutch mathematician
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Mathematica - The Principles of Math: 6.The Mysteries of Multiplication and Exponents
02:26 In 1856, Stevin expressed the number itself, its square, and its
cube using symbols.
02:27 (caption)
original number
its square
its cube
02:33 Legend has it that Stevin was quite a lazy mathematician who
couldn’t be bothered to write the same numbers over and over again.
That’s why he invented exponents.
02:46 (caption)
René Descartes (1596 –1650)
French philosopher and mathematician
02:46 In 1637, French philosopher and mathematician René Descartes
developed the expressions used for exponents.
02:54 The method of placing exponents to the upper right of the base
number was invented by Descartes and became the standard.
03:06 Whenever we have a base that is larger than 1, as the exponent
gets bigger, the result increases tremendously. We can get numbers
that boggle the mind.
03:21 (caption)
If you fold a newspaper page fifty times, how thick will it be?
03:27 Now, let’s try folding the page of a newspaper.
But it’s impossible to fold it fifty times, so we’ll pile it up instead of folding it.
03:40 Folding it once equals the thickness of two sheets of newspaper.
Folding it twice would equal four, folding it three times equals eight.
03:38 (caption)
folding once – two sheets piled up
folding twice – four sheets piled up
folding three times – eight sheets piled up
03:49 Each fold doubles how thick the pile of newspaper sheets is.
In other words, it can be expressed with exponents of the number two.
0359 (caption)
We have to fold it fifty times
One newspaper page is 0.1㎜ thick
04:01 So we fold it fifty times and each page is one-tenth of a
millimeter thick… That means the height of the pile will be…
04:13 112,590 thousand kilometers.
Sounds unbelievable, huh?
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Mathematica - The Principles of Math: 6.The Mysteries of Multiplication and Exponents
04:18 (caption)
20 = 1 sheet
21 = 2 sheets
04:19 But that’s the result we get from an accurate calculation.
Each time we multiply by two represents one fold, which is the same
as the number of times we added to the pile. Take a look at how high
the pile can go.
04:38 Folding it ten times makes it taller than a coffee cup.
04:42 Fifteen times and it’s taller than a refrigerator.
04:45 Twenty-two folds… and it’s as tall as a skyscraper.
04:54 At twenty-seven, it’s taller than Mt Everest.
04:56 (caption)
Mt Everest, 8848 meters
Mt Everest, 8.85 km
05:00 As you can see, the height of the newspaper pile keeps going
higher and higher… At fifty folds…it’s 112,590,000 kilometers, nearly
far enough to reach from Earth to Mars.
05:14 (caption) Mars
05:21 Now do you understand the power of exponents?
05:28 This is a Brahman temple in India. There are three columns here
and each holds sixty-four golden circular plates.
05:43 The Brahman monks trained themselves by moving those circular plates from one column to another. There are two rules for
achieving this.
05:49 (caption)
1. Only one plate can be moved at a time.
2. A larger plate must not be placed atop a smaller one.
06:00 In order to move all sixty-four plates, how many moves would
have to be made?
06:06 (caption) 1 plate: 1 move
06:14 How about two plates?
In this case, three moves are enough.
06:12 2 plates: 2 moves
06:22 How about three plates? Now we need seven moves.
06:22 3 plates: 7 moves
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Mathematica - The Principles of Math: 6.The Mysteries of Multiplication and Exponents
06:36 If we look closely, we notice a pattern with the number of moves
required.
06:43 The number of moves required is two to the power of the number of plates being moved, minus 1.
06:55 That means the number of moves for sixty-four circular plates
would be two to the power of 64, minus one (264 – 1).
And the answer is…Please, don’t be alarmed…
07:06 (caption) 264 – 1 = 18,446,744,073,709,551,615
07:07 How about that? That’s a pretty big number, pretty hard to even
read.
07:14 If one were to take one second for each move, how much time
would be required to move all the plates?
07:22 (caption) 584.9 billion years
07:23 Wow, that’s quite a long time. You’d get hungry.
Now if you started doing this around when the Earth was born, you’d
still be moving all those plates.
07:39 Exponents are useful for expressing extremely big or extremely
small numbers, especially in science.
07:45 (caption)
velocity of light
about 300,000,000 meters per second, or 3×108 ㎧
07:56 (caption)
size of hydrogen molecule
0.00000001㎝, or 1×10-8 ㎝
08:07 A cook is making noodles by hand. Every time he hits the flour
batter, the number of noodles increases.
08:14 The exponent principle, in which numbers increase tremendously, also applies here.
08:21 It begins with one lump of flour batter, but as he folds it, it becomes two, four, and then eight.
08:27 The number of noodles increases to two to the power of how
many times he’s folded the batter. In a short time, it becomes dozens
or hundreds. How can this be? We’re able to find the magical power of
exponents even in something like noodles!
08:46 Would you like to create a world full of kindness and warmth?
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Mathematica - The Principles of Math: 6.The Mysteries of Multiplication and Exponents
08:54 Do something to help three people around you. Those three then
help another three around them. Those nine then help another three,
and so on.
09:13 After ten rounds of this, sixty thousand people are helped.
After sixteen rounds, the entire population of Korea, about 50 million,
can be helped. After twenty-one steps, more than the entire population
of 7 billion will have been helped.
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